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This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for various phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have hardly been examined so far in the literature dedicated to singular perturbations. This book proposes to fill in this gap, since most applications are described by nonlinear models. Their asymptotic analysis is very interesting, but requires special methods and tools. The treatment presented in this volume comb

Boundary value problems --- Nonlinear boundary value problems. --- Singular perturbations (Mathematics) --- Asymptotic theory. --- Differential equations --- Perturbation (Mathematics) --- Asymptotic theory of boundary value problems --- Differential equations, Nonlinear --- Asymptotic theory --- Differential equations, partial. --- Partial Differential Equations. --- Partial differential equations --- Nonlinear boundary value problems --- Partial differential equations. --- Boundary value problems - Asymptotic theory

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We visualise developmental biology as the study ofprogressive changes that occurwithin cells, tissues and organisms themselves during their life span. A good exampleofa field ofdevelopmentalbiology in whichthis conceptis encapsulatedis thatofsomitogenesis. The somitewas identifiedas the primordialunit underlyingthe segmentedorganisationofvertebrates more than two centuries ago. The spectacular discoveries and achievements inmolecularbiologyin the last fifty years have created a gene-basedrevolution in both the sorts ofquestions as well as the approaches one can use in developmental biology today. Largely as a resultofthis, during the 20th and 21st centuries this simple structure, the somite, has been the focus ofa deluge ofpapers addressingmultipleaspectsofsomiteformation and patterning both at the cellularand molecular level. One ofthe mainreasons for suchinterest in the process ofsomitogenesis stems from the fact that it is such an exquisitelybeautiful example ofbiology working under strict temporal and spatial control in a reiterative manner that is highly conserved across the vertebrate classes. Our intention is that this book will be ofinterest to different kinds ofscientists, includingbasic researchers, pathologists, anatomists, teachersandstudentsworking in the fields ofcell and developmentalbiology. The nine chapterscoverawide array of topics that endeavour to capture the spirit of this dynamic and ever-expanding disciplineby integratingboth contemporaryresearchwith the classical embryological literaturethat concentratedon descriptionsofmorphologicalchanges inembryos and the interactionsofcells and tissues during development. Inso doingthey encompass the main aspects ofsomitogenesis across four vertebrate classes (frog, fish, mouse and chick) and the hope is that this will enable readers to acquire an appreciationof this developmentalprocess in all its facets.

biochemie --- Human biochemistry --- medische biochemie --- Diffraction --- Boundary value problems --- Problèmes aux limites --- EPUB-LIV-FT LIVBIOLO LIVBIOMO LIVMEDEC SPRINGER-B

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The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature. Such applications are discussed in the second part, and include semilinear elliptic problems on Rn, bifurcation from the essential spectrum, the prescribed scalar curvature problem, nonlinear Schrödinger equations, and singularly perturbed elliptic problems in domains. These topics are presented in a systematic and unified way.

Differential equations, Elliptic. --- Perturbation (Mathematics) --- Boundary value problems. --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Numerical analysis. --- Differential equations, partial. --- Functional analysis. --- Numerical Analysis. --- Partial Differential Equations. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Mathematical analysis --- Differential equations, Elliptic --- Partial differential equations.

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The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof; a bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques.

Mathematics. --- Functional Analysis. --- Operator Theory. --- Partial Differential Equations. --- Functional analysis. --- Operator theory. --- Differential equations, partial. --- Mathématiques --- Analyse fonctionnelle --- Théorie des opérateurs --- Scattering (Mathematics). --- Scattering (Physics) -- Mathematics. --- Waves -- Mathematics. --- Scattering (Physics) --- Scattering (Mathematics) --- Waves --- Scattering theory (Mathematics) --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Scattering --- Physics. --- Partial differential equations. --- Optics. --- Electrodynamics. --- Optics and Electrodynamics. --- Dynamics --- Physics --- Light --- Partial differential equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Classical Electrodynamics.

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The present monograph, based mainly on studies of the authors and their - authors, and also on lectures given by the authors in the past few years, has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading. Acknowledgements.TheauthorsthankL.E.Dubins,S.E.Graversen,J.L.Ped- sen and L. A. Shepp for useful discussions. The authors are grateful to T. B. To- zovafortheexcellenteditorialworkonthemonograph.Financialsupportandh- pitality from ETH, Zur ¨ ich (Switzerland), MaPhySto (Denmark), MIMS (Man- ester) and Thiele Centre (Aarhus) are gratefully acknowledged. The authors are also grateful to INTAS and RFBR for the support provided under their grants. The grant NSh-1758.2003.1 is gratefully acknowledged. Large portions of the text were presented in the “School and Symposium on Optimal Stopping with App- cations” that was held in Manchester, England from 17th to 27th January 2006.

Optimal stopping (Mathematical statistics) --- Boundary value problems. --- Nonlinear integral equations. --- Economics, Mathematical. --- Economics --- Mathematical economics --- Econometrics --- Mathematics --- Methodology --- Integral equations, Nonlinear --- Integral equations --- Nonlinear theories --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Optimal stopping (Mathematical statistics). --- Boundary value problems --- Nonlinear integral equations --- Economics, Mathematical --- Arrêt optimal (Statistique mathématique) --- Problèmes aux limites --- Equations intégrales non linéaires --- Mathématiques économiques --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Distribution (Probability theory. --- Mathematical optimization. --- Differential equations, partial. --- Finance. --- Probability Theory and Stochastic Processes. --- Calculus of Variations and Optimal Control; Optimization. --- Partial Differential Equations. --- Quantitative Finance. --- Funding --- Funds --- Currency question --- Partial differential equations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Calculus of variations. --- Partial differential equations. --- Economics, Mathematical . --- Isoperimetrical problems --- Variations, Calculus of --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk